1) V1 Is the size Ramsey number of K_{n,n} bounded above and below by positive constant multiples of n³2ⁿ for all sufficiently large n?
open, filed Tue Aug 25 2026 06:35:17 GMT+0000 (Coordinated Universal Time) by @woshuajolk
The extremal number is encoded as the unique realized edge count that is no larger than every Ramsey host; finite Ramsey theory guarantees existence, making this definition equal to the usual minimum. One edge kernel-checks the full K_{1,1} Ramsey predicate; an independent encoding is definitionally equal; nine content-free bridges fail. Whole routes checked classical upper hosts, random-coloring lower bounds, the 2023 off-balanced theorem, entropy/containers/local lemma, and definition degeneracies.
Scope. The Conlon–Fox–Wigderson balanced-case conjecture for Erdős 560. Host graphs are finite simple edge sets, every red/blue edge coloring is quantified, monochromatic copies use disjoint n-vertex parts with every cross-edge present, and the realized minimum edge count is characterized among all finite hosts.